Question

For three vectors `vecu, vecv, vecw` which of the following expressions is not equal to any of the remaining three?

Options

• `vecu.(vecv xx vecw)`

• `(vecv xx vecw).vecu`

• `vecv.(vecu xx vecw)`

• `(vecu xx vecv).vecw`

Answer 1

`bb(vecv.(vecu xx vecw))`

Explanation:

(1) `vecu.(vecv xx vecw) = [(vecu, vecv, vecw)]`

(2) `(vecv xx vecw).vecu = - vecv.(vecu xx vecw)`

= `-(vecv xx vecu).vecw`

= `vecu.(vecv xx vecw)`

= `[(vecu, vecv, vecw)]`

(3) `vecv.(vecu xx vecw) = -(vecu xx vecv).vecw`

= `-vecu.(v xx vecw)`

= `-[(vecu, vecv, vecw)]`

(4) `(vecu xx vecv).vecw = vecu.(v xx vecw) = [(vecu, vecv, vecw)]`

Clearly (3) is not equal